Announcements:

Current:

Review session for the final exam: Wednesday December 11, 12-2pm, in BIOL
2000.

Office hours after the end of term:

Thursday December 12, 10am -- noon

Friday December 13, 3-5pm.

Older:

With apologies, the office hours
on October 15 and 17 are cancelled, since I am away. The lectures are
happening this week at the usual times, of course. There will be
some extra office hours next week when I come back, please follow the
announcements.
With exam marking questions, please wait until I come back, and resist
asking Prof. Adams to change any marks.

September 24: In-class worksheet (distance between skew
lines) from September 24, with solutions, is here .

September 26/October 1: Here is the
contour
plot of a certain
function
f(x,y), that was discussed at the end of the class on Thursday September
26. There is a small prize for asking the best question about this plot
the next class (Tue, Oct. 1). Hint: look for things that are a bit weird
about this plot, and if anything seems strange, ask about it the next
class! The best questions and explanations will be posted here.
Sadly, the prize was not awarded.
One feature some people noticed was the strange behaviour of the plot near
the line y=-3x where the function is undefined.
However, no-one was surprised to see level curves meeting at a point
( here is a picture zoomed in
around that point; you can see the coordinates of the point on top).
Note that level curves can never have a common point in the domain of the
function; here the point at which they appear to "meet" is outside the
domain. What the picture shows is that the function f(x,y) approaches
different values as (x,y) approaches this point, depending on the curve
along which you are approaching. More about such phenomena is in 14.2
(which is not part of the course).
Another surprising feature is that we do not see any level curves in
a
certain region in the middle; on the other hand, every point in the domain
lies one some
level curve. What happens is, not all level curves are hyperbolas as it
seems; in fact, there are some ellipses in that region that initially
seemed empty -- you just have to force the computer to draw them. A couple
are pictured here
and here .

October 1: Please read
this post (by Joseph Lo) on tangent planes, and geometric meaning of
partial derivatives. It was discussed on October 1, and will be discussed
again on October 3. (You might have to log in with CWL to read it).

Required reading by Thursday
October 3: 14.3 and 14.4.

Required reading by Thursday October 10: 14.4 (was covered on October 8), 14.5 (we started it on Otober 8),
and 14.6 (will mostly talk about 14.6 on Thursday October 10, and will come back to 14.5 next week).